Comments about the “Exact Measurement” Concept

Since our physical world is a discontinuous one in which matter is an “agglomeration” of “nonhomogeneous” atoms (formed by nuclei, “void,” electrons), the surfaces of objects “seen” at atomic dimensions are not absolutely sharp. This fuzziness is increased by the thermal agitation of all constituents of matter. Therefore, “seen” at atomic dimensions, material surfaces are rather hazy. Consequently, no exact measurement of the length of an object is possible: the concept of exact measurement is not a physically realizable one. A corollary of this is that we cannot know the “exact” position of a particle. The application of these ideas to microphysical measurements shows that no simultaneous measurements of position and momentum are possible, quite apart from quantum theoretical considerations. But exact measurements are possible when we enumerate each element of a group by counting, because in this case we always have a “natural” unit to “measure” the group. What if we were to find a natural unit for length (or time)?